一阶中立型差分方程振动的充分必要条件

Necessary and Sufficient Conditions for Oscillation of First Order Neutral Difference Equations

本文研究了一阶常系数中立型时滞差分方程△[x(n)-px(n-τ)]+qx(n-σ)=0的振动性.当p>1时,通过构造若干适当的函数,我们分别得到了在τ-σ<1,(?)-σ=1和τ-σ>1三种情形下该方程振动的充分必要条件.

In this paper, oscillation of the first order neutral delay difference equation [x（n）-px（n-r）]＋qx（n-σ）=0with constant coefficients is studied, where p 〉 1.By constructing several suitable functions, the necessary and sufficient conditions, which guarantee the oscillation of this equation, are established for three cases t-σ〈1,t-σ=1 and t-σ〈1, respectively.